Question

factor completely.
4s + 20s³ + 15s² + 3

Explanation:

Step1: Rearrange the terms

First, we rearrange the polynomial \(4s + 20s^{3}+15s^{2}+3\) in descending order of the powers of \(s\):
\(20s^{3}+15s^{2}+4s + 3\)

Step2: Group the terms

We group the first two terms and the last two terms:
\((20s^{3}+15s^{2})+(4s + 3)\)

Step3: Factor out the GCF from each group

For the first group \(20s^{3}+15s^{2}\), the greatest common factor (GCF) of \(20s^{3}\) and \(15s^{2}\) is \(5s^{2}\). Factoring out \(5s^{2}\), we get:
\(5s^{2}(4s + 3)\)
For the second group \(4s + 3\), the GCF is \(1\), so it remains as \(1(4s + 3)\) or just \((4s + 3)\)

Step4: Factor out the common binomial factor

Now, we can see that both groups have a common binomial factor of \((4s + 3)\). Factoring out \((4s + 3)\) from the two terms:
\((4s + 3)(5s^{2}+1)\)

Answer:

\((4s + 3)(5s^{2}+1)\)